Strong-coupling study of the pairing mechanism in pressurized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>La</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi>Ni</mml:mi> <mml:mn>2</mml:mn> </mml:m

Recently, the bilayer perovskite nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ has been reported to exhibit high-temperature superconductivity near 80 K under a moderate pressure of about 14 GPa. To investigate the underlying pairing mechanism and symmetry in this complex system, we propose and analyze a mixed spin-1 and spin-$\frac{1}{2}$ bilayer $t\text{\ensuremath{-}}J$ model in the strong-coupling regime. This model explicitly incorporates the crucial role of strong Hund's coupling, which favors the formation of local spin-triplet states from the two on-site ${E}_{g}$ orbital electrons at half-filling. We further investigate the model using both slave-particle mean-field theory and the density matrix renormalization-group method. Our simulation results reveal that the dominant pairing channel is the interlayer one in the $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital. Hund's coupling is shown to enhance superconductivity within a reasonable physical range. Moreover, electron doping strengthens superconductivity by increasing carrier density; in contrast, hole doping weakens superconductivity. These findings offer critical insights into the unconventional superconductivity of pressurized ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ and underline the important role of orbital-selective behavior and Hund's rule.